# An aeroplane flys

1. Oct 19, 2009

### vorcil

An aeroplane takes off from (1,2,0) and climbs in the direction (-11,10,2)

part a) how close does the areo plane get to the top of an aerial mast at (0,2,1)

AB=b-a = (0,2,1)-(1,2,0) = (-1,0,1)

D(hat)= (-11,10,2)/15

AB.D(hat) = (11/15 + 2/15 = 13/15

root(AB - AB.D(hat)^2 )= root(2 - (13/15)^2)

=root(281)/15=1.1175
this is correct

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This is the part i'm having trouble with
PARTB)

Find the location of the areoplane after it has travelled 60km

60^2 = AB-AB.D(hat)
A = (1,2,0) B =(x,y,z)

what to do now?

2. Oct 20, 2009

### willem2

I don't understand what you're trying to do here. You can find a vector in the direction
of movement by subtracting (1,2,0) from (-11,10,2).
Then find the length of this vector and find a number to multiply the vector with, to
get the length equal to 60.
Finally add the vector to the starting point

3. Oct 20, 2009

### vorcil

Sorry I don't understand how you're way works any better!

subtracting 1,2,0 from -11,10,2????????
1,2,0 is a point
-11,10,2 is the direction of the line from that point

What do i do!!!!!!!!!!!

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1,2,0 - making up another point with 10(1,2,0)
a=1,2,0 b=10,20,0
AB=b-a (9,18,0)
|AB| = 20.124

60/20.124 = 2.981

2.981(9,18,0) = (26.83,53.66,0)

This is me trying to use your method above.

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The awnser is -43,32,8 but how do i get to it!

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Last edited: Oct 20, 2009
4. Oct 20, 2009

### vorcil

parametric equation(1,2,0)+t(-11,10,2)
components squared (1-11t)^2,(2+10t)^2+(2t^2) = 60^2

(1-11t)(1-11t) = (1-22t+121t^2)
(2+10t)(2+10t) =(4+40t+100t^2)
(4t^2)

sum the parts

t+18t+225t^2 = 60^2

I get
t=3.955
i'm rounding to 4

substituting
1-11t = x
2+10t = y
2t=z

1-44=-43
2+40=42
=8
(-43,42,8)

which is right according to the answers XD

5. Oct 20, 2009

### willem2

Sorry, I misread the question I tought the airplane went from (1,2,0) in the direction of the point (-11,10,2), but (-11,10,2) is already the direction of the line of travel.

You can find the length of (-11,10,2) and multiply this vector by (60/length)
to make its length equal to 60. Finally add it to the starting point.
If you do this you get the exact solution without any unjustified rounding of 3.955 to 4.
What you calculate, is the distance from (0,0,0) but what is asked is the distance travelled, so the distance from the starting point (1,2,0)